High Gas-Phase Methanesulfonic Acid Production in the OH-Initiated Oxidation of Dimethyl Sulfide at Low Temperatures

Dimethyl sulfide (DMS) influences climate via cloud condensation nuclei (CCN) formation resulting from its oxidation products (mainly methanesulfonic acid, MSA, and sulfuric acid, H2SO4). Despite their importance, accurate prediction of MSA and H2SO4 from DMS oxidation remains challenging. With comprehensive experiments carried out in the Cosmics Leaving Outdoor Droplets (CLOUD) chamber at CERN, we show that decreasing the temperature from +25 to −10 °C enhances the gas-phase MSA production by an order of magnitude from OH-initiated DMS oxidation, while H2SO4 production is modestly affected. This leads to a gas-phase H2SO4-to-MSA ratio (H2SO4/MSA) smaller than one at low temperatures, consistent with field observations in polar regions. With an updated DMS oxidation mechanism, we find that methanesulfinic acid, CH3S(O)OH, MSIA, forms large amounts of MSA. Overall, our results reveal that MSA yields are a factor of 2–10 higher than those predicted by the widely used Master Chemical Mechanism (MCMv3.3.1), and the NOx effect is less significant than that of temperature. Our updated mechanism explains the high MSA production rates observed in field observations, especially at low temperatures, thus, substantiating the greater importance of MSA in the natural sulfur cycle and natural CCN formation. Our mechanism will improve the interpretation of present-day and historical gas-phase H2SO4/MSA measurements.


S2. Chemistry mechanism for Box model 242
In this study, the basic gas-phase chemistry mechanism was based on MCMv3.3.1 23 and Hoffmann 243 et al., 2016 24 . Additionally, new reactions such as pathway 2b, the reaction of CH3SOH with O3; and 244 pathway 1b in which methylthiomethylperoxy radical (CH3SCH2OO, MSP) undergoes a fast 245 isomerization (Fig. 1); and the updated rate constants were implemented from previous studies 21, 25, 246 26, 27 . In summary, the DMS oxidation chemistry mechanism includes 75 species and 156 reactions 247 listed in Table S7. 248 As shown in Fig. 1, the first primary attack of OH radicals towards DMS proceeds via (1) a 249 hydrogen abstraction channel or (2) a reversible OH addition channel. The branching ratio of the 250 addition/abstraction channel decreases with increased temperature. Besides, we include (3)  251 heterogeneous reactions of DMS including O3 on the wall with semi-empirical reaction rate 252 coefficients. Heterogeneous reactions are the predominant source of DMSO2. Their contribution to 253 oxidation products (except DMSO2) is negligible compared to gaseous reactions. 254 In the hydrogen abstraction channel (1), after the H abstraction and consecutive O2 addition, MSP is 255 formed. It reacts further with hydroperoxyl radicals (HO2), peroxy radicals (RO2), or NOx 28 . The 256 reaction with NOx forming methyl thiomethoxy radical (CH3SCH2O) dominates the removal of 257 MSP 23,29 . In the previous studies 28 , the major primary oxidation products from MSP are 258 CH3SCHO and CH3SCH2O. Then the decomposition of CH3SCH2O and the reaction of CH3SCHO 259 with OH lead to methyl thiyl radicals (CH3S). CH3S is a critical compound in the following reaction 260 steps to form MSA and H2SO4. In the absence of O3 and NOx, O2 represents the possible reaction 261 partner for CH3S producing methyl thioperoxyl radical (CH3SO2), which undergoes an 262

S9
The application of a high-sensitivity detection instrumentchemical ionization mass spectrometers 269 improves our understanding of DMS chemistry kinetics. For example, a new intermediate product 270 hydroperoxymethyl thioformate (HOOCH2SCHO, HPMTF), was recently observed in the marine 271 atmosphere 21 and then simulated in laboratories 22,26 . These observations support the mechanism 272 (pathway 1b) proposed by Wu et al., 2015 25 . This mechanism starts from a fast intramolecular 273 hydrogen shift in MSP. Afterward, the new peroxy radical O2CH2SCH2OOH undergoes another 274 isomerization and decomposes to a stable intermediate product HPMTF. HPMTF further reacts with 275 OH or O3 to form SO2. The isomerization pathway (1b) changes the fate of MSP by competing with 276 biomolecular chemistry, especially at high temperatures. For example, the MSP isomerization is 277 predominant (≥ 95%) at +25 ℃. This suggests that the hydrogen abstraction channel plays an 278 important role at high temperatures. The isomerization reaction rate coefficient of MSP has been 279 determined to be 0.23 ± 0.12 s -1 at 295 ± 2 K 26 through flow tube experiments, 2.2 × 10 11 × exp(-280 9.8 × 10 3 / T) × exp(1.0 × 10 8 / T 3 ) from multi-conformer transition state theory (MC-TST) 281 calculation 21 , 0.09 s -1 (0.03-0.3 s -1 ) from a chamber study 22 , and 0.1 ± 0.05 s -1 from another flow 282 reactor study 30 . The isomerization reaction rates predicated by quantum chemical methods account 283 for the temperature dependency which is critical in this study. At 295 K, the theoretical calculation 284 gives a rate of 0.04 s -1 , which is around 2 to 5 times smaller than the experimental values. In this 285 study, we apply 2.2×10 11 × exp (-9.8 × 10 3 / T) × exp (1.0 × 10 8 / T 3 ) × f (f = 2-5) for the 286 isomerization reaction rate coefficient of MSP in the box model. Additionally, the overall error is 287 presented by grey shade in Fig. 3 by applying f = 1 to 5. 288 In the OH addition channel, the formation of OH-DMS adduct (CH3S(OH)CH3) is O2-dependent 289 and is well understood. DMSO and DMSO2 are formed from CH3S(O2)(OH)CH3 via 290 CH3S(OH)CH3 reaction with O2. The production of DMSO and DMSO2 is sensitive to NOx levels 291 due to the reaction of CH3S(O2)(OH)CH3 with NOx. Previous studies 31 also suggest that the 292 CH3S(O)(OH)CH3 adduct from DMSO and OH yields DMSO2 by reacting with O2. In this study, 293 we propose a small reaction rate coefficient for DMSO2 that is produced from DMSO oxidation 294 with OH, which is about 90 times lower than that of forming methanesulfinic acid (CH3S(O)OH, 295 MSIA). The further oxidation of DMSO2 is low (with OH, O3, or other oxidants), indicating its long 296 lifetime. MSIA is the primary oxidation product formed from DMSO that reacts with OH in the 297 absence and presence of NOx 32 . The previous studies 33,34 suggest that the reaction of MSIA and 298 OH in the gas phase forms SO2 only. However, the abstraction of an acidic H-atom by OH radicals 299 is typically slow because acidity implies a deficiency in electron density 35 . It is likely that OH adds 300 to the S-atom in MSIA, producing an intermediate product. It may decompose rapidly to form 301 S10 sulfurous acid (H2SO3) and CH3 36 or react with O2 producing MSA. But this pathway and its 302 reaction rate coefficients are not fully studied. Therefore, we treat the reaction of MSIA with OH 303 forming CH3S(O)2 in our box model; it either decomposes to SO2 or reacts with O3 yielding MSA 304 31,37 . Consequently, both the addition and abstraction pathways contribute to MSA production via 305 the reaction of MSIA with OH. The formation of DMSO and MSIA is the dominant pathway in the 306 OH addition channel. Also, the DMSO will react with OH producing aqueous MSIA in the aqueous 307 phase, which can further form aqueous MSA via reacting with OH 24, 38 . However, both the gaseous 308 MSIA and MSA show wall loss lifetime in the CLOUD chamber, so we would suggest that they are 309 unlikely to be produced from the wall. But we cannot completely rule out the aqueous-phase 310 reactions of DMSO with OH and MSIA with OH. We also include pathway 2b for the OH addition 311 channel, in which the oxidation of methane sulfenic acid (CH3SOH) by OH or O3 forms SO2 or 312 CH3SO. CH3SOH is an intermediate product formed from the decomposition of OH-DMS adduct 313 (CH3S(OH)CH3) 31 . In this study, the reaction with O3 is the dominant sink for CH3SOH because 314 the O3 concentration is much higher than that of OH (a factor of thousands), but the difference 315 between these two reaction rates is small and does not exceed a factor of 25, while the reaction with 316 OH is faster. 317 As discussed above, HO2 influences the DMS oxidation pathway via several reactions; and it is 318 critical at low temperatures when the isomerization reaction slows down. In this case, the increased 319 HO2 can reduce HPMTF formation by enhancing bimolecular reactions. Besides, HO2 enhances 320 MSA formation in the final reaction step of CH3SO3 with HO2 via competing with thermal 321 decomposition. These determine the importance of HO2 simulation, which will be discussed in the 322 next section. 323 The adopted mechanism here introduces an additional way via DMSO oxidation to MSIA, which 324 increases MSA production. MSA is produced almost exclusively from the reaction of CH3SO3 with 325 HO2 through abstraction pathway 1a and addition pathway 2a. The fraction of MSA can be 326 presented by the production rates of CH3S(O)2 formation. CH3S(O)2 formed from 1) CH3SO2 or 327 CH3SO in the abstraction pathway 1a, MSIA produced from the addition pathway further reacts 328 with 2) OH and NO3 radicals, and 3) DMSO2 reacts with OH. At -10 ℃, MSIA reacts with OH is 329 the dominant pathway to form CH3S(O)2. Although DMSO2 is high, the reaction rate coefficient of 330 DMSO2 with OH is low, 1 × 10 −14 molecule -1 cm 3 s -1 , leading to a production rate of ~1 × 10 3 s −1 331 cm −3 . While it still needs to undergo two more steps to form CH3S(O)2, thus, the formation of 332 CH3S(O)2 from DMSO2 is tiny. The production rate for CH3S(O)2 formed from the abstraction 333 pathway is around 3× 10 3 s −1 cm −3 . While the production rate for MSIA and OH forming CH3S(O)2 334 is ~1× 10 5 s −1 . Therefore, around 90% of the MSA is formed from addition pathway 2a at -10 ℃. S11 In the model, H2SO4 is formed from SO3 and the oxidation of SO2 with OH. Our model suggests 336 that the dominant source of H2SO4 is SO3, which is produced by the thermal decomposition of 337 CH3SO3 and the reaction of MSIA with OH. There has been no report of any direct experimental 338 evidence for the formation of SO3 in DMS oxidation. However, field observation notes that the 339 measured H2SO4 could not be explained by oxidation of SO2 with OH only 39 . In this study, we do 340 not have experimental evidence to prove the occurrence of reactions, but if occurring, it would be 341 important. SO2 is formed mainly through three pathways: 1) pathway 1a, decomposition of 342 CH3S(O)2; 2) pathway 2b, the reaction of CH3SOH with O3; 3) pathway 1b, the further oxidation of 343 HPMTF. 344

S3. HO2 and OH in the box model 345
As mentioned before, HO2 and OH are important, which were not measured but simulated in the 346 box model based on the chamber parameters of temperature, relative humidity, DMS, O3, CO, NOx 347 concentration, and O3 photolysis rate. HO2 is produced from the reactions of OH with O3, CO, H2, 348 NO3, and loss by reacting with NO2, O3, and DMS oxidation products. Considering the reaction rate 349 constants and the conditions of our experiments, OH, O3 and CO are the primary parameters that 350 determine HO2 concentration and its uncertainty. In this study, we applied the direct measurements 351 of O3 and CO to our box model, which increases the accuracy of HO2 simulation. The employed Br -352 -MION-CIMS and Br --FIGAERO(g)-CIMS in different experiment sets can measure HO2. However, 353 HO2 is not calibrated, and its detection efficiency strongly depends on relative humidity therefore, 354 direct HO2 measurement is not available. 355 Although OH measurement was not available, the estimated concentration in the box model is well 356 simulated. In the box model, OH is believed to be a wall loss species according to the mobility 357 calculation from He et al., 2021 40 . Besides, the most critical parameter for estimated OH 358 concentration is the photolysis rate from UV lights; we calibrated them between different 359 campaigns via the calibration experiment of H2SO4 formed from the oxidation of SO2 by OH. We 360 always used the same amount of SO2, O3, H2O, CO, and lights and employed the same NO3 --CIMS 361 measuring H2SO4. The OH production ( ) can be calculated by the following equations (Eq 9-362 11) and agree with each other within certain uncertainty, as shown in the previous campaign. The 363 OH production is used to estimate the photolysis rate of O3 that is applied in the box model. 364 Therefore, we would like to assume the OH concentrations are well evaluated in the box model. 365 Eq11 368

S4. Heterogeneous wall reactions of DMS and O3 369
The negligible decay of DMSO and DMSO2 during the dark stage in Fig. 2 strongly suggests a dark 370 source producing DMSO and DMSO2, which requires only DMS, O3, and H2O. This occurs on 371 walls 41,42 . Fig. S 11 shows the wall reactions of DMS and O3 in the first 155 minutes of an 372 experiment starting with clean conditions and turn-off UV lights (before the vertical dotted line). In 373 this case, DMSO appears when DMS is injected (with a nearly constant O3 mixing ratio at ~ 34 374 ppbv) and increases rapidly from 8 × 10 6 to 2.3 × 10 8 cm -3 . DMSO2 appears 15 minutes later than 375 DMSO and increases from 2.3 × 10 7 to 1.6 × 10 9 cm -3 . The different overall shapes versus time 376 (linear and quadratic) and the time delay indicate that DMSO2 is a second-generation product from 377 the first-generation product DMSO. We plot time sequences of DMSO and DMSO2 after DMS 378 injection on a linear scale in Fig where DMS+O 3 wall = 3.4 × 10 -18 molec -1 cm 3 s -1 and DMSO+O 3 wall = 3 × 10 -15 molec -1 cm 3 s -1 , at + 386 25 ℃ and 24 % RH in the CLOUD chamber. This is likely aqueous-phase oxidation of DMS 24, 42 , 387 in this case with wall-adsorbed water. A similar process may well occur in aerosol water and 388 droplets in the marine atmosphere, and the implication of the reaction rate constants needs to be 389 modified depending on the conditions. However, the reaction rate constant for the DMSO reaction 390 is about 103 times higher than for the DMS reaction with O3, which is inconsistent with the results 391 in Gershenzon et al., 2001 43 . This opposite behavior might be explained by other chemical reactions 392 besides ozonolysis or a catalytic effect of stainless steel on the chemical reactions as has been 393 observed previously for hydroperoxides 44 . This is, however, speculation as we have no clear 394 evidence for such a process. Except for O3, halogen species like Br, Cl, and I2 and their oxidation 395 species can also react with DMS. However, none of them were introduced in the chamber and 396 neither has been detected by our mass spectrometers. Therefore, these two semi-empirical reaction 397 rate constants are surrogates for the possible reactions noted above and should only be used for S13 accounting for DMS and DMSO wall reactions in this study specifically and should not be used for 399 atmospheric simulations. In this study, we are not able to investigate the temperature or RH 400 dependence for these two semi-empirical parameters with only one experiment. While the constant 401 DMSO2 concentration in the temperature ramping experiment 2 ( Fig. S 14) shows that the 402 heterogeneous reactions have a weak temperature dependence over that range. Aside from DMSO 403 and DMSO2, we see no evidence that wall reactions have influenced the other oxidation products in 404 the dark experiment. DMSO and DMSO2 are the only two oxidation products showing production 405 in the dark, indicating there is no direct formation of other oxidation products from wall reactions 406 with DMS and O3 only. Fig. 2 also shows that all the other products exhibit either rapid wall loss or 407 in the case of CH3SCHO, ventilation loss only. The CLOUD walls present an effective 408 condensation sink of 2 × 10 -3 s -1 , which is 5-7 times higher than those reported for the pristine 409 Marine Boundary Layer 45 but is within the range typically observed in coastal areas 46, 47 . With 410 lights on (after the dotted line), the OH-initiated DMS gas-phase oxidation commenced, leading to 411 higher production rates for both DMSO and DMSO2. In this case, subtracting the wall reactions, the 412 production from OH-initiated DMS oxidation and the loss to OH radicals control the appearance 413 time of DMSO and DMSO2. We find DMS+OH→DMSO gas = 1.2 × 10 -12 molec -1 cm 3 s -1 and 414 DMSO+OH→DMSO 2 gas = 1 × 10 -12 molec -1 cm 3 s -1 by fitting the time series of DMSO and DMSO2.  where DMSO w and DMSO 2,w refer to gaseous DMSO and DMSO2 formed from heterogeneous wall 431 reactions. To determine these two rate coefficients, it is assumed that the adsorbed DMS and O3 on 432 the walls are proportional to gaseous DMS and O3, respectively. In this case, we simulated the time 433 series of DMSO and DMSO2 by solving the differential equations Eq 3 and Eq 4 with an initial 434 random guess for the parameters ( DMS+O 3 wall , DMSO+O 3 wall ) using the function ODEINT in 435 Python. After that, we evaluated the simulated results by applying the least-squares -the sum 436 squared difference between the simulated ( ; ) and measured data points . 437 problem, is applied to find the best solution (here referring to the parameters). A basic iteration 441 includes updating the parameter ′ randomly in the range of (0,1) and calculating its corresponding 442 ′ . Then the system considers the neighboring and decides between moving the system to ′ or 443 staying in . 444 We apply a loss to evaluate the parameters: when < 0, and are replaced by ′ and ′ , 446 when > 0, and will be replaced within certain possibilities (Metropolis probability). 447 The same analysis was applied to determine DMS+OH→DMSO gas and DMSO+OH→DMSO 2 gas in the 448 experiment which includes wall and gas-phase reactions. Here, the equations change to: 449 where DMSO g and DMSO 2,g refer to gaseous DMSO and DMSO2 formed from gas-phase and 456 heterogeneous wall reactions. DMSO+OH gas = 8.9 ×10 -11 cm 3 s -1 , DMSO 2 +OH gas = 4.4 ×10 -14 cm 3 s -1 , 457 taken from MCMv3.3.1, and loss is ventilation loss, 1.6 ×10 -4 s -1 in experiment set 3. 458

S5. Temperature effect on DMS oxidation products 459
MSA has a stronger temperature dependence than H2SO4. As shown in Fig. S 14, when the 460 temperature decreases from +25 to +10 °C (Exp 2), the MSA concentration increases by an order of 461 magnitude from 8 × 10 5 to 1.4 × 10 7 cm -3 , while the H2SO4 concentration increases only by a factor 462 of 1.5 compared to its initial concentration. The formation of H2SO4 from SO2 reacting with OH 463 radical depends on temperature; however, this effect is small compared to the exponential 464 temperature function of thermal decomposition. At the same time, various intermediates increase by 465 various factors: MSIA 60 %, CH3SCHO a factor of 1.9, CH3SOH 87 %, CH3S(O)2OOH a factor of 466 6.8, and DMSO a factor of 1.3. This is consistent with the mechanism in collision-induced dissociation of the MSIA clusters sets in at higher voltages than the used 21V and 540 the dissociation of the NH3NH4 + cluster, suggesting that the MSIA cluster ions are strongly bound 541 and thus ionized at the kinetic limit, furthermore the gas-phase basicity appears strong enough for 542 MSIA to keep the proton upon collision-induced dissociation at high voltages. This is not the case 543 for HPMTF, but it also dissociates at higher voltages than the used 21V in both ionization schemes. 544 3.4 × 10 -18 molec -1 cm 3 s -1 and + = 3 × 10 -15 molec -1 cm 3 s -1 are used here for the 566 simulation of the dark and photo-oxidation experiment. The subtle increase in DMSO time trace 567 when UV lights were turned on is a consequence of substantially increased production from OH + 568 DMS in the gas phase and substantial loss, again via OH (~ 5 × 10 -4 s -1 ). 569 570 571 572 S24 573

Fig. S 12. The correlation between [MSA] and a) [MSIA], b) [CH3SCHO], c) [HPMTF], d) 574
[CH3SOH]. The triangles present the data collected from steady-state conditions of different OH-575 initiated DMS oxidation experiments listed in  and OH concentrations are kept constant at 100 pptv and 7 × 10 6 cm -3 . NO2 and NO are kept 625 constant at zero. Note that, in the atmosphere, these representative total concentrations of MSA, 626 H2SO4, and other species will at least partially condense and/or partition into the atmospheric 627 aerosol, reducing gas phase concentrations. 628 629 We set 120 ppbv as the background value for simulation when the measurement is missing. b refers to the estimated OH concentration from the box model. c the DMS concentrations here are modeled values.

CIMS No
a Here, we cannot measure the loss for DMSO and DMSO2 since the heterogeneous reactions happened on the wall all the time. We assume they are ventilation loss products in this study because they are not able to be lost to the wall rapidly due to the wall reactions.   6.5×10 9 1×10 9 -10 CLOUD chamber Field measure ment 4 a n/a n/a n/a n/a 1×10 6 -4×10 7 2×10 5 -7×10 6 n/a n/a -10 to -6 Ny-Ålesund 5 b 0.1-0.5 n/a n/a n/a n/a n/a 2.5×10 8 -3×10 9 3×10 9 -5×10 9 n/a Arabian Sea 6 c n/a n/a n/a n/a 3.5×10 7 -6.8×10 7 n/a n/a n/a −10 to 5 over Southern Ocean 7 d n/a 0-2×10 6 n/a n/a 0-6.5×10 6 0-1.4×10 7 n/a n/a Abov e 10 Mace Head 8 e n/a n/a n/a n/a 2×10 6 -